We present an experimental study of low temperature electronic transport in the hybridization gap of inverted InAs/GaSb composite quantum wells. An electrostatic gate is used to push the Fermi level into the gap regime, where the conductance as a function of sample length and width is measured. Our analysis shows strong evidence for the existence of helical edge modes proposed by Liu et al [Phys. Rev. Lett. 100, 236601 (2008)]. Edge modes persist in spite of sizable bulk conduction and show only a weak magnetic field dependence-a direct consequence of a gap opening away from the zone center.